Students going into fourth grade at Harvard Kent Elementary School attend summer school, in August, in Boston. Two international studies show fourth- and eighth-grade scores in math, science, and reading in 2011, from the latest data released Tuesday.

“When you look at the US scores, those scores are solid,” says Tom Loveless, a senior fellow at the Brookings Institution, who also notes that there is still a lot of room for improvement, particularly on math and science. “There shouldn’t be complacency, but there also shouldn’t be alarmist rhetoric.”

The two tests released Tuesday, both with 2011 data, were the Trends in International Mathematics and Science Study (TIMSS), which measures math and science achievement for fourth- and eighth-graders around the world, and the Progress in International Reading Literacy Study (PIRLS), which measures fourth-grade reading.

Quickly distilling the results to a simple ranking – or looking at how the US moved in the rankings from the last TIMSS test, given in 2007 – is complicated. Not only are there varying grade and subject levels, but a number of educational “systems” participate in the test, including several US states and places like Hong Kong that don’t quite achieve “nation” status – and the list of participating countries is a little different each time.

That said, in some cases, the US stacked up fairly well against other countries and educational systems, particularly on PIRLS, where the US average score of 556 was significantly higher than the international average, set at 500.

The US scored lower in the reading study than did five educational systems (Hong Kong, the state of Florida, the Russian Federation, Finland, and Singapore), was statistically equal to seven others, and was higher than 40.

More striking (particularly given that in US measurements, reading scores have been harder to improve than math scores), the US average improved an impressive 16 points from the last time the test was given in 2006. And in terms of the percentages of students scoring at or above the most “advanced” reading benchmark score, only two systems – Singapore and Florida – were ahead of the United States.

In the TIMSS math and science scores, the results for the US were more mixed. The US average score increased by a measurable amount in fourth-grade math, but remained statistically unchanged in fourth-grade science and eighth-grade math and science.

The US average was higher than the international average in all subjects, but, as with the domestic report card scores, students’ performance seemed to fall with older students.

Eight education systems (including the state of North Carolina) scored better than the US in fourth-grade math, while by eighth grade, 11 outscored the US (including Massachusetts, Minnesota, North Carolina, and Indiana).

In science, the US fell even more rapidly: Just six education systems outscored the US in fourth grade, and by eighth grade, 12 had higher average scores.

“What we see in our national assessment is improvement among our youngest kids,” notes Jack Buckley, commissioner of the National Center for Education Statistics, which released the data. “But when you start looking at our older students, you see less improvement over time.” Those results, he says, are mirrored here, as well as in the other major international comparison, PISA, which tests 15-year-olds, and on which the US tends to fare more poorly than on TIMSS.

"These new international comparisons underscore the urgency of accelerating achievement in secondary school and the need to close large and persistent achievement gaps," US Education Secretary Arne Duncan said in a statement. "Learning gains in fourth grade are not being sustained in eighth grade."

As has been the case in past years, several Asian countries and systems, in particular, shine in math.

In fourth-grade math, for instance, 43 percent of Singapore students, and 39 percent of Korean students, reached the highest “advanced” benchmark – compared with just 13 percent of US students.

"A number of nations are out-educating us today in the STEM disciplines," noted Secretary Duncan. "And if we as a nation don’t turn that around, those nations will soon be out-competing us in a knowledge-based, global economy."

What’s also notable is who isn’t among the very top scorers – most notably, Finland.

Based largely on its strong showing in the PISA (for Programme for International Student Achievement) scores, Finland has become a focal point for a number of education experts, who believe the US should use its system as a model.

But in the TIMSS data – especially on math – Finland wasn’t all that different from the US.

“Finland’s scores in math are statistically a dead heat” with the US, “which shows you how fragile that reputation, which is exaggerated, is,” says Mr. Loveless – who notes that Finland’s eighth-grade math scores have actually declined since Finland last took TIMSS, in 1999.

On PISA, for instance, Korea outscored Finland in eighth-grade math by just five points, but on TIMSS, it was 99 points higher. (The two tests use the same scale.)

The explanation, in large part, lies in the difference between the two tests, both of which have their advocates. PISA, which surveys 15-year-olds (regardless of the grade they are in), tries to measure how well students can apply knowledge. TIMSS tries to measure students’ knowledge.

Loveless (a TIMSS advocate) believes that TIMSS is the better measure of what schools around the world are doing – but more important, he notes, the differences between the two tests point to the pitfalls of basing too much in any single measure, or to cherry pick only certain data.

“The truth is that really the US does mediocre on math and science, and does quite well on PIRLS [reading], but we have a lot of room for improvement,” he says.

The 2011 TIMSS data also offer some insight into states: nine states participated at the eighth-grade level, and Florida and North Carolina also participated at the fourth-grade level. (Only Florida participated in the PIRLS fourth-grade reading.)

And some of those states did well, outperforming the US average.

At the eighth-grade level, Massachusetts, Minnesota, North Carolina, and Indiana scored above the US average in math, and Massachusetts, Minnesota, and Colorado scored above the US average in science. (California and Alabama scored below the US average in both tests, and several other states weren’t measurably different.)

In eighth-grade science, only Singapore had a higher percentage of students reaching the “advanced” benchmark than the state of Massachusetts.

“For the US overall, our average performance is pretty respectable,” says Mr. Buckley. “But it’s interesting to see that among those states that volunteer [to take part in the test] we have some states performing among the highest systems in the world."

Duncan, in his assessment, was even more pointed, saying the strong showing of highly diverse states like Florida, Massachusetts, and North Carolina shows that "demography is not destiny in our schools."